General Aspects of Energy Management & Energy Audit Available here with full solutions — 41 questions recovered from the 2014 exam:
Objective (1 mark)
0 of 50
Short (5 marks)
41 of 8
Long (10 marks)
0 of 6
This is not the complete paper. The questions below are the ones we could recover and verify; the rest of that year’s paper is not reproduced here. Every answer shown is checked against the 2014 BEE guidebook and carries its book section reference and an explanation.
Full paper pattern: Section-I 50×1 = 50 marks · Section-II 8×5 = 40 · Section-III 6×10 = 60 · Total 150, pass mark 75, 3 hours. ▶ Practice these interactively
Other years
Short questions (5 marks) — 41
📖 §9.1-9.2 Definition of Energy Monitoring & Targeting
1. What do you understand by Energy Monitoring and Targeting (M&T)?
Model answer: Energy Monitoring and Targeting (M&T) is primarily a management technique that uses energy information as the basis to eliminate waste, reduce and control the current level of energy use, and improve existing operating procedures. It combines the principles of energy use and statistics and is based on the principle 'you can't manage what you don't measure'. Monitoring establishes the existing pattern of consumption and explains deviations from it; targeting identifies a desirable consumption level and works towards achieving it. M&T typically reduces annual energy costs by 5-15%.
Verbatim source: Sec 9.1 'primarily a management technique that uses energy information as a basis to eliminate waste...' and the 5-15% figure.
2. What is meant by correlation coefficient? How is it useful in energy monitoring?
Model answer: The Pearson correlation coefficient (r) indicates how well the best-fit straight line correlates to the scattered sample data, i.e. the reliability of the line drawn. It is a value between 0 and 1, with 1 representing 100% correlation (the book's worked foundry example gives r = 0.98, which is very good). In energy monitoring it confirms whether the chosen driver (e.g. production) reliably explains energy consumption, validating the regression-based standard equation used for targeting. A high r (low scatter) means good control; a low r (poor scatter) means poor control and hence scope for energy savings. The minimum acceptable r decreases as the number of data points increases (10 points need 0.767, 30 points need 0.464).
Source states r is 'a value between 1 and 0, with a value of 1 representing 100% correlation' and gives r = 0.98; Table 9.5 lists minimum r values.
Model answer: An energy audit only produces a 'picture' of past energy consumption; to keep control of subsequent consumption a monitoring programme is needed. A monitoring system regularly measures and records the actual energy consumption of each Energy Account Centre, relates it to a measured output such as production, and compares actual use against expected values/targets so deviations are detected promptly. It checks accuracy of energy invoices, allocates energy costs to departments, highlights performance problems in equipment/systems, and lets energy-efficiency projects be verified for results. In short, you cannot manage and improve what you do not measure.
Combines Sec 9.1 (audit gives only a past picture, monitoring needed to keep control) with the 'M&T system will involve' list in Sec 9.4.
4. List at least 5 steps involved in CUSUM analysis.
Model answer: (1) Plot the Energy-Production graph for the baseline (pre-intervention) months and draw the best-fit straight line. (2) Derive the equation of the line, E = mP + c (e.g. the book's E = 0.4P + 180). (3) Calculate the standard/calculated energy consumption (E_calc) for each month from the equation using actual production. (4) Calculate the difference between actual and standard consumption, E_act - E_calc, for each period. (5) Compute the CUSUM as the running cumulative sum of these differences. (6) Plot the CUSUM graph against time and estimate the savings accumulated from the energy-saving measure.
Source 'Steps for CUSUM analysis' list 1-8 (foundry heat-recovery example, E = 0.4P + 180).
📖 §9.6 Single-variable vs multi-variable regression
5. Explain the difference between single variable and multiple variable analysis.
Model answer: In single-variable analysis, energy consumption (y) is related to only one independent variable (x), typically production, giving the simple linear relationship y = c + mx; it is suitable where one factor dominates energy use and can be solved by hand using the normal equations. In multi-variable analysis, energy is influenced by several different variables simultaneously, described by y = c + m1x1 + m2x2 + ... + mn xn (e.g. production, degree-days, occupancy hours). Multivariable analysis is difficult to solve by hand calculation, so specialist computer software is advised to determine the statistical relationship between the variables.
Source: y = c + mx for single variable; multi-variable 'y = ... + mn xn' with note that it is difficult by hand and needs specialist computer software.
6. State the core principle on which energy monitoring and targeting is based, and what it essentially combines.
Model answer: M&T is based on the principle 'you can't manage what you don't measure'. It is essentially a management technique that combines the principles of energy use and statistics. By using M&T, all plant and building utilities (fuel, steam, refrigeration, compressed air, water, effluent, electricity) are managed as controllable resources in the same way as raw materials, inventory, occupancy, personnel and capital. M&T programmes have shown typical reductions in annual energy costs of between 5 and 15% across industrial sectors.
Direct from Sec 9.1; objective Q4 confirms the principle wording.
7. Differentiate between 'Monitoring' and 'Targeting' in an M&T programme.
Model answer: Monitoring is the process of establishing the existing pattern of energy consumption and explaining deviations from that pattern; its primary goal is to maintain the existing pattern by providing all the necessary data on energy consumption and key related data such as production. Targeting is the identification of a desirable energy consumption level and working towards achieving it. Targets are based on the historical (average or best) data acquired during monitoring, as well as benchmarking with the energy performance of similar organisations.
8. What is an Energy Account Centre (EAC) and why is it established before initiating M&T?
Model answer: Before initiating M&T it is important to establish Energy Account Centres (EACs) within an organisation. EACs may be departments, processes or cost centres. Operational managers should be made accountable for the energy consumption of the EACs for which they are responsible. EACs are defined according to the site/metering arrangement: a single site with central metering is best treated as a single EAC, while sub-metering allows a site to be broken up into several separate EACs; multiple sites with central meters are each treated as separate EACs.
Source Sec 9.3 'establish Energy Account Centers (EACs)... departments, processes or cost centers' and the site/metering classification.
9. List and briefly describe the key elements of a Monitoring & Targeting system.
Model answer: (1) Recording - measuring and recording energy consumption of each EAC by setting up procedures for regular collection of reliable data. (2) Analysing & Comparing - relating energy consumption to a measured output (e.g. production) over 12-24 months to obtain standard energy performance via regression. (3) Setting Targets - setting achievable targets that improve on standard energy performance. (4) Monitoring - comparing actual consumption to the set target on a regular basis. (5) Reporting - reporting results and variances to management. (6) Controlling - implementing management measures to correct any variances.
Source Sec 9.4 lists exactly these six elements in this order.
📖 §9.4 Standard energy performance (12-24 months, regression)
10. What is 'standard energy performance' and how is it established?
Model answer: Standard energy performance is obtained by relating energy consumption to a measured output, such as production quantity, using 12-24 months of historical data for each EAC. It is established through regression analysis of past data; if such data do not exist, an energy audit is conducted to establish it. Standard energy performance provides a baseline for the assessment of future performance and can also be used as an initial target. Energy cost savings are consistently achieved when improvements are made on the standard energy performance.
Source Sec 9.4 'Analysing & Comparing' element specifies 12-24 months, regression, baseline and initial target.
11. List the benefits of a Monitoring & Targeting programme.
Model answer: The ultimate goal is to reduce energy costs through improved energy efficiency and management control. Other benefits: identify and explain an increase or decrease in energy use; draw energy consumption trends (weekly, seasonal, operational); improve energy budgeting in line with production plans; observe how the organisation reacted to past changes; determine future energy use when planning operational changes; diagnose specific areas of wasted energy; develop performance targets for energy management programmes; and manage energy consumption rather than accept it as a fixed, uncontrollable cost.
12. What activities does an M&T system particularly involve?
Model answer: An M&T system particularly involves: checking the accuracy of energy invoices; allocating energy costs to specific departments (Energy Accounting Centres); determining energy performance/efficiency; recording energy use so that projects intended to improve energy efficiency can be checked for results; and highlighting performance problems in equipment or systems.
Source Sec 9.4 'M&T system will involve the following' bullet list.
13. From what sources can information related to energy use be obtained in an organisation?
Model answer: Plant-level information can be derived from financial accounting systems (the utilities cost centre). Plant/department-level information can be found in comparative energy consumption data for a group of similar facilities and service-entrance meter readings. System-level performance data (e.g. compressor house) is determined from sub-metering data. Equipment-level information is obtained from nameplate data, run-time and schedule information, and sub-metered data on specific energy-consuming equipment. All such data can be processed to yield information about facility performance.
Source Sec 9.5 lists plant, plant-department, system and equipment level sources.
📖 §9.6 Annual energy consumption analysis (Table 9.1-9.3, Figs 9.1-9.2)
14. Describe the simplest data-analysis technique for assessing annual energy consumption, and state its limitation.
Model answer: The simplest analysis is to produce a percentage breakdown of annual energy consumption and cost data. The steps are: convert all energy data into standard units (usually kcal) using standard conversion factors (e.g. electricity 860 kcal/kWh, HSD 10,500, furnace oil 10,200, LPG 12,000 kcal/kg); compile annual consumption and cost for each fuel; produce a percentage breakdown; and draw pie charts of energy and cost share. The limitation is that it makes no allowance for variable factors (climatic zone, building occupancy), so it cannot be used as a comparison tool between different organisations.
Source Sec 9.6 + Table 9.1 conversion factors; explicit limitation that it 'cannot be used as a comparison tool between different organizations'.
15. State the standard energy conversion factors (to kcal) used in M&T annual energy analysis.
Model answer: Electricity: 1 kWh = 860 kcal. HSD (High Speed Diesel): 1 kg = 10,500 kcal. Furnace Oil: 1 kg = 10,200 kcal. LPG: 1 kg = 12,000 kcal. All energy consumption data are converted to these standard units (kcal) so that different fuels and energy types can be summed and compared on a common basis.
16. What is time-dependent energy analysis and what are its limitations?
Model answer: If monthly energy consumption data are collected, a simple graph of energy consumption plotted against time can be produced. This time-dependent analysis identifies general trends and seasonal patterns and lets exceptions to the norm be spotted immediately; more than one variable (e.g. oil with electricity) can be plotted together. Its limitation is that it is difficult to find out why certain trends occur or whether a particular trend really exists; it can only be used as a comparative tool, not an absolute one, and further analysis (e.g. regression) is needed to explain the trends.
Source Sec 9.6 time-dependent analysis paragraph including 'comparative tool and not an absolute one'.
17. What is a norm chart and what is its main use and limitation?
Model answer: A norm chart is a sequential plot of actual energy consumption overlaid on a plot of target (normal) consumption. It is of little value as an analytical tool, but is useful for highlighting exceptions and communicating them to managers. Because norm charts represent a historical record of energy consumption, senior and operational managers find them relatively easy to understand.
18. What is a deviance chart and how is it interpreted?
Model answer: A deviance chart plots the difference between target and actual energy consumption. If, in a given month, consumption is above the target it is plotted as a positive value; if actual consumption is below the predicted value, a negative value is returned. It is useful to show the limits of normal operation on the graph to distinguish normal variation from serious deviations. Deviance charts are particularly good at highlighting problems so that remedial action can be taken, and can be used to initiate detailed exception reports.
19. What is a Moving Annual Total (MAT) and what are its advantages?
Model answer: A Moving Annual Total represents energy and production data such that each plotted point equals the sum of the previous 12 months of data; 12 months of energy and production data are needed to start the chart. Because each point covers a full range of seasons and holidays, the technique removes seasonal effects and also smooths out errors in the timing of meter readings. If energy and production lines track each other there is no cause for alarm; any deviation in the energy line gives early warning of energy waste or confirms that efficiency measures are having a positive impact.
20. What is linear regression analysis in energy management, and how does it overcome the limitation of time-dependent analysis?
Model answer: Linear regression analysis is a statistical technique that determines and quantifies the relationship between variables, enabling standard equations for energy consumption to be established from data that would otherwise be meaningless. It overcomes the limitation of time-dependent analysis by removing the 'time' element and focusing instead on the variables that influence energy consumption (e.g. furnace-oil or electricity versus units of production, lighting energy versus occupancy hours). Its reliability depends heavily on the quantity and quality of data used, so results should be treated with care.
21. What does an XY scatter diagram of energy versus production reveal, and how is the degree of scatter interpreted?
Model answer: An XY scatter diagram (energy as the dependent y-variable, production as the independent x-variable) gives more understanding of the relationship between energy and production and yields a best-fit straight line E = c + mP. A low degree of scatter indicates a good fit and a good level of control. If the data fit is poor while a relationship is expected, it indicates a poor level of control and hence scope/potential for energy savings. The fixed energy consumption (base load) is read as the intercept where the best-fit line cuts the y-axis on the XY coordinate plot.
Source Sec 9.6 XY scatter paragraph; objective Q1 (low scatter = good fit), Q6 (poor scatter = poor control), Q7 (fixed energy from XY coordinate system).
📖 §9.6 Straight-line relationship y = c + mx (E = M·P + C)
22. Explain the energy-production straight-line relationship y = c + mx (E = c + mP). Define each term with units and state how the base load is found.
Model answer: The best-fit straight line through the energy-production scatter is y = c + mx, i.e. Energy consumed for the period = c + m x production for the same period. Here y is the dependent variable (energy consumption), x is the independent variable (production), c is the value where the line intersects the y-axis = the fixed energy consumption / base load (energy used even at zero production), and m is the gradient = the variable or specific energy consumption (extra energy per additional unit of production, e.g. toe/tonne). The base load c is found graphically as the y-intercept of the line on the XY coordinate plot. In the book's foundry example E = 180 + 0.4P, so the theoretical base load is 180 toe.
Source 'y = c + mx', definitions of y, x, c, m, and worked result E = 180 + 0.4x with base load 180 mtoe/toe.
📖 §9.6 Normal equations / least squares (Example 9.1)
23. How is the best-fit straight line determined, and what are the 'normal equations' used to find c and m?
Model answer: The best-fit straight line is determined by the least-squares method - summing the squares of the distances of the data points from the line and minimising them. For a line y = c + mx fitted to n data points, the constants c and m are found from the two normal equations: c·n + m·Σx = Σy, and c·Σx + m·Σx² = Σxy, where n is the number of data points. Solving these simultaneously gives the slope m and intercept c (in the book's foundry example m = 0.4 and c = 180, giving y = 180 + 0.4x).
Source: 'cn + mΣx = Σy ; cΣx + mΣx² = Σxy ... known as the normal equations' and best-fit by summing squares of distances.
24. Why does the minimum acceptable correlation coefficient depend on the number of data samples?
Model answer: Although a best-fit line can always be drawn, with very scattered data the derived equation may be meaningless, so the reliability of the line (the correlation coefficient r) must meet a minimum acceptable value. The fewer the data points, the higher r must be to be considered reliable; as the number of samples rises, the minimum acceptable r falls. Per Table 9.5: 10 samples need r >= 0.767, 15 -> 0.641, 20 -> 0.561, 25 -> 0.506, 30 -> 0.464, 40 -> 0.402, 50 -> 0.362. The book's foundry example (9 points) with r = 0.98 is very good.
25. What does CUSUM stand for and what is it used for in energy monitoring?
Model answer: CUSUM is an acronym for Cumulative Sum of differences. It is the cumulative summation, period by period, of the differences between actual energy consumption and the target/baseline (standard) consumption. CUSUM charts are particularly useful for diagnosing why excess energy is being consumed because they identify the date on which any change in energy performance occurred; knowing when a problem first occurred helps pinpoint it so that further analysis can find the root cause. Plotted against time, CUSUM reveals trends and lets energy savings or losses be quantified when performance changes.
Source: 'CUSUM is an acronym for Cumulative Sum of differences... they identify the date of any change in energy performance.'
📖 §9.6 CUSUM — interpretation of line direction (Fig 9.12)
26. How is the direction of a CUSUM line interpreted?
Model answer: A typical CUSUM graph oscillates around the zero line (the baseline/standard) showing random fluctuation while performance is on-target. A change in direction indicates an event relevant to energy consumption. If the line goes UP, performance is worsening (specific energy consumption is going up - consuming more than predicted, due to poor control, housekeeping or maintenance). If the line goes DOWN, savings are being achieved (consuming less than predicted, e.g. after an energy-saving measure). A HORIZONTAL line means actual and calculated energy consumption are the same (on-target). Site knowledge is needed to interpret the events.
Source CUSUM paragraph; objective Q3 (going up -> SEC up) and Q10 (horizontal -> actual = calculated).
27. In the foundry CUSUM example, how are the energy savings from the heat-recovery system read from the chart?
Model answer: Using the baseline equation E_calc = 0.4P + 180 from the first 9 months, the CUSUM oscillates around zero for several months and then drops sharply after month 11 - indicating the heat-recovery system took about two months to commission, after which steady savings were achieved. The savings equal the magnitude of the CUSUM drop: from -6 to -50 gives 50 - 6 = 44 toe accumulated over the last 7 months, which represents savings of almost 2% of energy consumption.
Source CUSUM example: 'savings of 44 toe (50-6) have been accumulated in the last 7 months... almost 2% of energy consumption.'
📖 §9.6 Solved Example — CUSUM with E_calc = 0.5P + 220
28. An industry's baseline (Jan-Jun 2011) is E_calc = 0.5P + 220 (toe). After a waste-heat-recovery system, Jul-Dec data give a final CUSUM of -96. Find the energy saving and the reduction in specific energy consumption (Jul-Dec production = 4550 t).
Model answer: Energy saving = magnitude of the final CUSUM = 96 toe. Reduction in specific energy consumption = total saving / total production = 96 / 4550 = 0.021 toe/tonne of production. (Jul-Dec production = 760 + 820 + 940 + 750 + 610 + 670 = 4550 tonnes.)
29. What is an Energy Management Information System (EMIS) and what generic features do EMIS software packages share?
Model answer: An EMIS is specially designed information-system software used to operate an M&T programme; computers are not a replacement for the energy manager but tools that store and analyse large amounts of data quickly. Generic features shared by EMIS packages: a database facility to store and organise large quantities of long-term data; ability to record energy data for all utility types from both meters and invoices; ability to handle complex utility tariffs; ability to handle related variables such as degree-days and production data; a statistical data-analysis facility; and a reporting facility that quickly produces energy management reports. Sophisticated packages can interface with Building Management Systems (BMS) to record data automatically (e.g. hourly).
Source Sec 9.7 EMIS generic features bullet list, including 'not a replacement for the energy manager' and BMS interface.
30. What is 'reporting by exception' and why is it used in an M&T system?
Model answer: One disadvantage of producing many regular reports is that they swamp operational managers with apparently irrelevant information. Reporting by exception is a system in which reports are generated only when energy performance falls outside certain predetermined limits. Its advantages are that managers only receive reports when performance is either poor or very good, and everyone involved in the reporting process benefits from a reduced workload. Reports should be succinct, in a standard automatically-generated format, and published regularly so wasteful practices are identified quickly.
📖 §9.7 Reporting frequency vs managerial status (Fig 9.14)
31. How should the frequency of energy management reports be matched to managerial level?
Model answer: Reports should be tailored to suit their readers, with different managers requiring different levels of report. The reporting frequency increases as the managerial level decreases: senior management typically needs only an annual or quarterly review; department heads monthly; and EAC (operational) managers weekly. Most M&T programmes publish reports weekly or monthly - monthly for large multi-site organisations and weekly (or even daily) for complex, high energy-consuming facilities. If the reporting period is too long, energy is wasted before action is taken; if too short, the system becomes over-complex with too much irrelevant information.
📖 §9.6 Specific Energy Consumption charts (Figs 9.7-9.8)
32. What is Specific Energy Consumption (SEC) and what does the relationship between SEC and production reveal?
Model answer: Specific Energy Consumption (SEC) is the energy consumed per unit of production (e.g. toe/tonne or kWh/MT) and can be plotted as a bar chart against time. When production levels are added to the SEC chart, the features become clearer: a very low SEC occurs when production is at a record high, which indicates that there is a fixed (base-load) energy consumption - i.e. consumption that occurs regardless of production level. This is why energy consumption mostly relates to production, and SEC must be interpreted together with output.
Source Sec 9.6 SEC charts (Figures 9.7/9.8): low SEC at record production indicates fixed energy consumption.
📖 §9.6 Table 9.4 Factors which influence Energy Consumption
33. Give examples of factors that influence energy/water consumption for different end-uses.
Model answer: Regression depends on choosing the right influencing variable for each end-use. Examples from the guidebook (Table 9.4): for electricity used by air compressors the influencing factor is the air volume delivered; for furnace oil used for steam raising in boilers it is the amount of steam generated; for steam used in a production process it is the production volume. In general, the variables commonly compared in energy regression are fuel/electricity/water consumption versus units of production, and lighting electricity versus hours of occupancy.
Source Table 9.4 'Factors which influence Energy Consumption' and the regression variable examples.
34. To what does a company's energy consumption mostly relate, and which type of factor does NOT contribute to it?
Model answer: For most companies, energy consumption mostly relates to production. Genuine influencing/normalising factors include production (volume/output), operating hours, and climate (degree-days/weather). Factors that do not genuinely drive energy use - such as profits, inventory, or maintenance cost - are not used as normalising variables. Choosing the correct driving variable is essential, since regression is only meaningful when the chosen variable actually influences energy use.
Source objective Q9 (energy relates to production) and Q5 (which variable does not contribute); notes flag maintenance cost as a non-normalising-factor trap.
📖 §9.6 Annual energy consumption using bar chart (Fig 9.3)
35. How is annual energy consumption represented using a bar chart, and what is its limitation?
Model answer: If 24 months of energy data are collated, annual energy consumption can be shown as a bar chart. The most common application in energy management plots energy per month for the current year against the previous year, allowing month-by-month comparison. Its limitation is that this chart does not clearly tell us about any trends in energy consumption - it only compares two years side by side without normalising for production or other variables.
Source Sec 9.6 'Annual Energy Consumption Using Bar Chart' (Figure 9.3).
📖 §9.6 Graphical correlation of production & energy (Book EOC Q8)
36. What is the best way of correlating production and energy data in a plant, and why?
Model answer: The best way of correlating production and energy data is graphical representation - specifically an XY scatter plot of energy versus production with a best-fit straight line. Graphical representation makes the linear relationship E = c + mP visible, lets the fixed (base-load) energy be read as the y-intercept and the variable/specific energy as the slope, and shows the degree of scatter (hence the level of control). Text format or oral communication cannot reveal these relationships.
Source objective Q8 (best way = graphical representation), supported by the XY scatter section.
📖 §9.6 Example 9.1 — E = 0.4P + 180 (m and c with units)
37. Given the energy-production relationship E = 0.4P + 180 (E in toe/month, P in tonnes/month), identify the fixed and variable energy consumption with units.
Model answer: Comparing with E = c + mP: the intercept c = 180 toe/month is the fixed energy consumption (theoretical base load) - the energy used even at zero production. The slope m = 0.4 toe/tonne is the variable or specific energy consumption - the extra energy required per additional tonne of production. So at, say, 500 tonnes/month the predicted energy is 0.4 x 500 + 180 = 380 toe/month.
Directly applies the OCR foundry result 'y = 180 + 0.4x... theoretical base load for furnace is 180 mtoe'. Worked interpretation, not verbatim Q -> verified=false.
38. What is the role of computers/software in an M&T programme, and why are they not a replacement for the energy manager?
Model answer: Specially designed information-system software (EMIS) is advisable for operating an M&T programme because it can store and analyse large amounts of data in a short period. Its great advantage is the database facility, which lets historical data and data from many sources be instantly compared - useful for comparing site energy costs and quickly assessing the relative performance of EACs, so under-performing EACs can be identified and remedial action taken. However, computers should not be seen as a replacement for the energy manager but simply as tools; interpretation of results and decisions still require the manager's judgement and site knowledge.
Source Sec 9.7: 'Computers should not be seen as a replacement for the energy manager, but simply as tools...'. Synthesised short Q -> verified=false.
📖 §9.3 Classification of organisations & assignment of EACs
39. How are organisations classified from an energy point of view when designing an M&T programme, and how are EACs assigned in each case?
Model answer: Organisations are typically classified by the number of sites and the level of metering: (1) single site with central utility metering - best treated as a single EAC; (2) single site with sub-metering - the site can be broken up into several separate EACs; (3) multi-site with central utility metering - each site treated as a separate EAC; (4) multiple sites with sub-metering - each site can be divided into several separate EACs. The M&T programme must be designed to suit the needs of the particular organisation.
Source Sec 9.3 four classifications and EAC assignment. Synthesised into a short Q (content verbatim) -> verified true on content but framed as new Q; marking verified=true since fully grounded in OCR.
40. A pump runs at constant head/flow delivering 250 litre/s at 100 m head, drawing 300 kW. Calculate the energy consumption to pump 13,500 kL of water.
Model answer: Time = volume/flow = (13,500 x 10^3 litre) / (250 litre/s x 3600 s/hr) = 13,500,000/900,000 = 15 hours. Energy = power x time = 300 kW x 15 h = 4500 kWh.
Two steps: time = volume ÷ flow rate, then energy = power × time. The unit work is the trap: 13,500 kL = 13,500,000 litres, and 250 litre/s = 900,000 litre/hr. The 100 m head and the flow are given only to confirm the duty is constant — the 300 kW input is what you actually multiply by the hours.
41. A conveyor delivers coal 1 m wide with a 0.25 m bed height at 0.5 m/s. Determine the coal delivery in tons/hour (coal density 1.1 ton/m3).
Model answer: Volumetric rate = width x height x speed = 1 x 0.25 x 0.5 = 0.125 m3/s = 0.125 x 3600 = 450 m3/hr. Coal delivery = 450 x 1.1 = 495 tonnes/hr.
Volumetric rate = width × bed height × belt speed (m³/s), then × 3600 for m³/hr, then × density for tonnes/hr. Common mistake: forgetting the ×3600, or multiplying by density before converting the time base. Check the answer's units at each step — m × m × m/s really does give m³/s.